Pilot study of the relation between various dynamics of avatar experience and perceptual characteristics

In recent years, due to the prevalence of virtual reality (VR) and human-computer interaction (HCI) research, along with the expectation that understanding the process of establishing sense of ownership, sense of agency, and limb heaviness (in this study, limb heaviness is replaced with comfort level) will contribute to the development of various medical rehabilitation, various studies have been actively conducted in these fields. Previous studies have indicated that each perceptual characteristics decrease in response to positive delay. However, it is still unclear how each perceptual characteristic changes in response to negative delay. Therefore, the purpose of this study was to deduce how changes occur in the perceptual characteristics when certain settings are manipulated using the avatar developed in this study. This study conducted experiments using an avatar system developed for this research that uses electromyography as the interface. Two separate experiments involved twelve participants: a preliminary experiment and a main experiment. As observed in the previous study, it was confirmed that each perceptual characteristics decreased for positive delay. In addition, the range of the preliminary experiment was insufficient for the purpose of this study, which was to confirm the perceptual characteristics for negative delay, thus confirming the validity of conducting this experiment. Meanwhile, the main experiment showed that the sense of ownership, sense of agency, and comfort level decreased gradually as delay time decreased, (i.e., this event is prior to action with intention, which could not be examined in the previous study). This suggests that control by the brain-machine interface is difficult to use when it is too fast. In addition, the distribution of the most strongly perceived settings in human perceptual characteristics was wider in regions with larger delays, suggesting this may lead to the evaluation of an internal model believed to exist in the human cerebellum. The avatar developed for this study may have the potential to create a new experimental paradigm for perceptual characteristics.


METHODS
Details of the used methods are present in the main manuscript.Method details considered as appendix material are as follows.
There were "comparison settings": gain 2, 0.45, 0.7, 0.95}.Meanwhile, the fourth questionnaire was designed to investigate the discrimination thresholds in which participants were asked whether there was a difference in the sensations of avatar control experience (whether they feel avatar movement as a "lack of movement" (−) or "hyper responsive movement" (+)), and rated their experience on a worst to best scale from "−3 to +3" compared to the standard setting (0) in "0.25" increments.

Examples of System Response
Examples of the avatar system's responses to the NMSS model inputs are shown in Figure 10.As indicated in the figure, gain contributes to movement intensity, damping coefficient contributes to overshoot respectively.

Discrimination threshold
The respective evaluated values and effect size with an asterisk indicate the size of those shown in Figure 11 and     Table 4.
• For gain, the larger the comparison setting value, the more positive (felt "hyper responsive movement") the evaluated value was.In addition, all of the effect sizes were "large." • For natural angular frequency, the smaller the comparison setting value, the more negative (felt "lack of movement") the evaluated value was.The effect size for ω np1 -ω np2 was "medium," and all other effect sizes were "large." • For the damping coefficient, the larger the comparison setting value, the more negative the evaluated value (felt "lack of movement").In addition, all of the effect sizes were "large." • In dead time, when the comparison setting value shifted from L 1 to L 2 , the evaluated value was biased toward positive (felt "hyper responsive movement") and thereafter toward negative (felt "lack of movement").The effect size for L 1 -L 2 and L 3 -L 4 were "medium," while the effect size for L 2 -L 3 and L 2 -L 4 were "large.".31* Figure 11: Discrimination threshold: evaluated value; natural angular frequency axis was reversed to be consistent with the dead time direction.The smaller the natural angular frequency, the larger the delay.However, because natural angular frequency range was narrow, its axis is not log scale.

Gain
The evaluated value and effect size in gain are shown in Figure 12 and Table 5.
• SoO values tended to be convex downward.The effect size of K 3 − K 4 was "medium." • SoA values did not change effectively, regardless of the change in comparison setting value.Meanwhile, there was no effect size indicating "medium" or "large." • CL values did not change effectively in the range of and K 1 − K 3 were "medium." Table 5: Gain in the preliminary experiment: effect sizes (upper: SoO, middle: SoA, and lower: CL) .10 .25 K 3 .32* .11 .03.14K 2 .15 .02K 3 .17 .41* .36*.26K 2 .06 .06K 3 .03 Figure 12: Gain in the preliminary experiment: evaluated value

Damping Coefficient
The evaluated values and effect sizes for the damping coefficient are shown in Figure 13 and Table 6.
• SoO values increased as the comparison setting value increased.The effect size of ζ 3 − ζ 4 was "medium," and all other effect sizes were "large.".11 Figure 13: Damping coefficient in the preliminary experiment: evaluated value the effect sizes for K 1 − K 2 , K 2 − K 3 , and K 3 − K 4 , each of which compares adjacent comparison settings, only K 1 − K 2 showed anything greater than "medium."Therefore, the tendency for the value to increase from K 1 to K 2 may be considered effective.
The range of gain in this study suggested that CL was impaired when gain was small, but gain had no effect on SoO or SoA.Gain is a parameter of movement intensity.Above a certain intensity, SoO, SoA, and CL are not affected, while only comfort is impaired at the lower intensity than a certain intensity.This suggests that CL may be a more acute questionnaire to the perceptions of changes in the target behavior than SoA.

Damping Coefficient
SoO increased as the comparison setting value increased.The effect size of The damping coefficient is a parameter of overshoot.These results indicate that the low damping coefficient, which cause a larger overshoot, make SoO, SoA, and CL decrease, while the high damping coefficient, which causes a smaller overshoot, make SoO, SoA and CL increase.However, it indicates that overshoot affects only SoO in the low overshoot area.These results indicate that it has the possibility that the trend of generating SoO in overshoot differs from SoA and CL.

SoA at Dummy Setting
Similar to natural angular frequency and dead time, for gain and damping coefficient, SoA was higher than 0 in the dummy setting, which is the same case as in the standard setting.This suggests that SoA may be improved by repetition compared to the other perceptual characteristics, since the participants always experience the avatar in each setting after experiencing the standard setting due to the experimental protocol.In contrast, CL is introduced as the alternative parameter of limb heaviness in order to allow questions not only about the feeling of heaviness, but also about the feeling of lightness, based also on reports that comfort is related to SoA [3].SoA is changed from this result and CL may be a more acute questionnaire method in some cases.

and ζ 3 −
ζ 4 , which compare adjacent comparison settings, respectively shows "large," "large," and "medium."SoA increased as the comparison setting value increased.The effect sizes of ζ 1 − ζ 2 , ζ 2 − ζ 3 , and ζ 3 − ζ 4 , which compare adjacent comparison settings, respectively show "large," "large," and "small."Thus, this trend in the range of ζ 1 ≤ ζ i ≤ ζ 3 may be effective.However, this trend in the range of ζ 3 ≤ ζ i ≤ ζ 4 is hardly effective.In other words, SoA increased by increasing the damping coefficient in the low damping coefficient area, but has no effect on SoA in the high damping coefficient area.CL increased with increasing value in the range of ζ 1 ≤ ζ i ≤ ζ 3 and decreased with increasing value in the range of ζ 3 ≤ ζ i ≤ ζ 4 .The effect sizes of ζ 1 − ζ 2 , ζ 2 − ζ 3 , and ζ 3 − ζ 4 , which compare adjacent comparison settings, respectively, show "large," "large," and "small."Thus, this trend in the of range ζ 1 ≤ ζ i ≤ ζ 3 may be effective.However, this trend in the range of ζ 3 ≤ ζ i ≤ ζ 4 is hardly effective.In other words, CL increased by increasing the damping coefficient in the low damping coefficient area, but has no effect on CL in the high damping coefficient area.The results of SoO and CL indicate that these have the possibility that the trend of generating SoO in the damping coefficient differs from SoA and CL.